Im trying to fix my posture - so looking at the miror - i think that when i pull my chest up it helps improve my posture - so it will help me to know what muscles help pull the chest up - (imagine someone taking a big breath and trying to look as big as possible - he pulls his chest up)

its probobly some back muscles im trying to think which ones maybe some shoulder ones

but what do you think about this - is the pectoralis minor one of the muscles i need to work on ?

I have exactly the same issue, but maybe not for the same cause. I've worked a lot on infraspinatus and traps, I think they help to keep my shoulders straight, and spinal erectors to avoid middle back curvature which I think it's the final the cause for my chest being concave.

My posture is still bad but it has improved a lot. I don't think it as a matter of working isolated muscles, but entire the upper body.

Seated mid-rows are probably your exercise of choice, really make the effort to squeeze your shoulder blades together. Lean forward so that the angle at your hips is just under 90 degrees, and keep your elbows in close to your body. Sitting up straight will involve more of your lats, which won't have as much of an effect on posture (but are still important for overall back health).

Also good posture is very much a habit thing, so when you're walking around but especially whenever you do any exercise at all, make sure you keep your shoulder blades squeezed tight, your shoulders down, and your chest up.